
import numpy as np
import pandas as pd
import math
import seaborn as sns
import matplotlib
import matplotlib.pyplot as plt
from scipy.stats import pearsonr
from sklearn import tree
from sklearn import linear_model
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import train_test_split
from sklearn.metrics import explained_variance_score
from time import time
from sklearn.metrics import r2_score
import os


from google.colab import drive
drive.mount('/content/drive')

Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount("/content/drive", force_remount=True).


data = pd.read_csv('/content/drive/MyDrive/kc_house_data.csv')
from sklearn.preprocessing import MinMaxScaler
from sklearn.feature_selection import RFE
from sklearn.linear_model import LinearRegression
import statsmodels.api as sm
from statsmodels.stats.outliers_influence import variance_inflation_factor

/usr/local/lib/python3.7/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.
  import pandas.util.testing as tm


data.head(20)


data.describe()


years = []
for i in range(data.shape[0]):
  years.append(data.date[i][0:4])


data['years']  = [int(i) for i in years]


data.head()


data['age'] = data['years'] - data['yr_built']
data.head()


updated_age = []
for i in range(data.shape[0]):
  if data.yr_renovated[i] == 0:
    temp = data.age[i]
  else:
    temp = data.years[i] - data.yr_renovated[i]
  updated_age.append(temp)


data['updated_age'] = updated_age


data.head()


data.dtypes

id                 int64
date              object
price            float64
bedrooms           int64
bathrooms        float64
sqft_living        int64
sqft_lot           int64
floors           float64
waterfront         int64
view               int64
condition          int64
grade              int64
sqft_above         int64
sqft_basement      int64
yr_built           int64
yr_renovated       int64
zipcode            int64
lat              float64
long             float64
sqft_living15      int64
sqft_lot15         int64
years              int64
age                int64
updated_age        int64
dtype: object


data = data.drop(['id','date', 'years', 'yr_built', 'yr_renovated', 'zipcode'], axis = 1)


#Check any number of columns with NaN or missing values
empty_col = data.isnull().any().sum()
print('total no. of columns which have any Null value : {}'.format(empty_col))

total no. of columns which have any Null value : 0


# Check any number of data points with NaN
empty_rows = data.isnull().any(axis=1).sum()
print('total no. of rows which have any Null value : {}'.format(empty_rows))

total no. of rows which have any Null value : 0


from sklearn.preprocessing import MinMaxScaler
from sklearn.feature_selection import RFE
from sklearn.linear_model import LinearRegression
import statsmodels.api as sm
from statsmodels.stats.outliers_influence import variance_inflation_factor

data.head()


sns.pairplot(data)
plt.show()


data.plot(kind='scatter', x = 'sqft_living', y = 'price');
plt.show()


data.plot(kind='scatter', y = 'price', x = 'bathrooms');
plt.show()


data.plot(kind='scatter', y = 'price', x = 'updated_age');
plt.show()


data.plot(kind='scatter', y = 'price', x = 'age');
plt.show()


data.plot(kind='scatter', y = 'price', x = 'condition');
plt.show()


h = data.hist(bins=25,figsize=(16,16),xlabelsize='10',ylabelsize='10',xrot=-15)


sns.countplot(data.bedrooms, order = data['bedrooms'].value_counts().index)

/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  FutureWarning

<matplotlib.axes._subplots.AxesSubplot at 0x7f9e29641610>


sns.countplot(data.view, order = data['view'].value_counts().index)

/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  FutureWarning

<matplotlib.axes._subplots.AxesSubplot at 0x7f9e27313e50>


sns.countplot(data.waterfront, order = data['waterfront'].value_counts().index)

/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  FutureWarning

<matplotlib.axes._subplots.AxesSubplot at 0x7f9e27778550>


sns.countplot(data.grade, order = data['grade'].value_counts().index)

/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  FutureWarning

<matplotlib.axes._subplots.AxesSubplot at 0x7f9e3d713510>


sns.countplot(data.age, order = data['age'].value_counts().index)

/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  FutureWarning

<matplotlib.axes._subplots.AxesSubplot at 0x7f9e27689790>


data.columns

Index(['price', 'bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors',
       'waterfront', 'view', 'condition', 'grade', 'sqft_above',
       'sqft_basement', 'lat', 'long', 'sqft_living15', 'sqft_lot15', 'age',
       'updated_age'],
      dtype='object')


f, axe = plt.subplots(1, 1,figsize=(10,5))
sns.boxplot(x=data['bedrooms'],y=data['price'],ax=axe)
f, axe = plt.subplots(1, 1,figsize=(15,5))
sns.boxplot(x=data['bathrooms'],y=data['price'],ax=axe)
f, axe = plt.subplots(1, 1,figsize=(12,5))
sns.boxplot(x=data['floors'],y=data['price'],ax=axe)

'''f, axe = plt.subplots(1, 1,figsize=(12,5))
sns.boxplot(x=data['sqft_living'],y=data['price'],ax=axe)
f, axe = plt.subplots(1, 1,figsize=(12,5))
sns.boxplot(x=data['sqft_lot'],y=data['price'],ax=axe)
f, axe = plt.subplots(1, 1,figsize=(12,5))
sns.boxplot(x=data['waterfront'],y=data['price'],ax=axe)
f, axe = plt.subplots(1, 1,figsize=(12,5))
sns.boxplot(x=data['view'],y=data['price'],ax=axe)
f, axe = plt.subplots(1, 1,figsize=(12,5))
sns.boxplot(x=data['condition'],y=data['price'],ax=axe)
f, axe = plt.subplots(1, 1,figsize=(12,5))
sns.boxplot(x=data['grade'],y=data['price'],ax=axe)
f, axe = plt.subplots(1, 1,figsize=(12,5))
sns.boxplot(x=data['sqft_above'],y=data['price'],ax=axe)
f, axe = plt.subplots(1, 1,figsize=(12,5))
sns.boxplot(x=data['sqft_basement'],y=data['price'],ax=axe)
f, axe = plt.subplots(1, 1,figsize=(12,5))
sns.boxplot(x=data['lat'],y=data['price'],ax=axe)
f, axe = plt.subplots(1, 1,figsize=(12,5))
sns.boxplot(x=data['long'],y=data['price'],ax=axe)
f, axe = plt.subplots(1, 1,figsize=(12,5))
sns.boxplot(x=data['sqft_living15'],y=data['price'],ax=axe)
f, axe = plt.subplots(1, 1,figsize=(12,5))
sns.boxplot(x=data['sqft_lot15'],y=data['price'],ax=axe)'''

"f, axe = plt.subplots(1, 1,figsize=(12,5))\nsns.boxplot(x=data['sqft_living'],y=data['price'],ax=axe)\nf, axe = plt.subplots(1, 1,figsize=(12,5))\nsns.boxplot(x=data['sqft_lot'],y=data['price'],ax=axe)\nf, axe = plt.subplots(1, 1,figsize=(12,5))\nsns.boxplot(x=data['waterfront'],y=data['price'],ax=axe)\nf, axe = plt.subplots(1, 1,figsize=(12,5))\nsns.boxplot(x=data['view'],y=data['price'],ax=axe)\nf, axe = plt.subplots(1, 1,figsize=(12,5))\nsns.boxplot(x=data['condition'],y=data['price'],ax=axe)\nf, axe = plt.subplots(1, 1,figsize=(12,5))\nsns.boxplot(x=data['grade'],y=data['price'],ax=axe)\nf, axe = plt.subplots(1, 1,figsize=(12,5))\nsns.boxplot(x=data['sqft_above'],y=data['price'],ax=axe)\nf, axe = plt.subplots(1, 1,figsize=(12,5))\nsns.boxplot(x=data['sqft_basement'],y=data['price'],ax=axe)\nf, axe = plt.subplots(1, 1,figsize=(12,5))\nsns.boxplot(x=data['lat'],y=data['price'],ax=axe)\nf, axe = plt.subplots(1, 1,figsize=(12,5))\nsns.boxplot(x=data['long'],y=data['price'],ax=axe)\nf, axe = plt.subplots(1, 1,figsize=(12,5))\nsns.boxplot(x=data['sqft_living15'],y=data['price'],ax=axe)\nf, axe = plt.subplots(1, 1,figsize=(12,5))\nsns.boxplot(x=data['sqft_lot15'],y=data['price'],ax=axe)"


data_lot = data[data['sqft_lot'] < data['sqft_living']]


data = data.drop(list(data_lot.index), axis = 0)


data1 = data.copy()


import numpy as np
bed_per = np.percentile(data1.bedrooms, np.arange(0,101,10))
for i in range(len(bed_per)):
  print("{} percentile value is {}".format(i*10, bed_per[i] ) )

0 percentile value is 0.0
10 percentile value is 2.0
20 percentile value is 3.0
30 percentile value is 3.0
40 percentile value is 3.0
50 percentile value is 3.0
60 percentile value is 4.0
70 percentile value is 4.0
80 percentile value is 4.0
90 percentile value is 4.0
100 percentile value is 33.0


bed_per = np.percentile(data1.bedrooms, np.arange(90,101,1))
for i in range(len(bed_per)):
  print("{} percentile value is {}".format(i, bed_per[i] ) )

0 percentile value is 4.0
1 percentile value is 5.0
2 percentile value is 5.0
3 percentile value is 5.0
4 percentile value is 5.0
5 percentile value is 5.0
6 percentile value is 5.0
7 percentile value is 5.0
8 percentile value is 5.0
9 percentile value is 6.0
10 percentile value is 33.0


for i in np.arange(0.0, 1.0, 0.1):
    var = data1["bedrooms"].values
    var = np.sort(var,axis = None)
    print("{} percentile value is {}".format(99+i,var[int(len(var)*(float(99+i)/100))]))
print("100 percentile value is ",var[-1])

99.0 percentile value is 6
99.1 percentile value is 6
99.2 percentile value is 6
99.3 percentile value is 6
99.4 percentile value is 6
99.5 percentile value is 6
99.6 percentile value is 6
99.7 percentile value is 6
99.8 percentile value is 7
99.9 percentile value is 8
100 percentile value is  33


data[data.bedrooms == 8]


data.drop(data.loc[data['bedrooms']>= 8].index, inplace=True)


data2 = data.copy()


scaler = MinMaxScaler() 
arr_scaled = scaler.fit_transform(data2)
norm_data = pd.DataFrame(arr_scaled, columns = data2.columns , index=data2.index)
plt.figure(figsize = (30, 25))
sns.heatmap(norm_data.corr(), annot = True, cmap="YlGnBu")
plt.show()


data = data.drop(['age','sqft_above'], axis = 1)


data.columns

Index(['price', 'bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors',
       'waterfront', 'view', 'condition', 'grade', 'sqft_basement', 'lat',
       'long', 'sqft_living15', 'sqft_lot15', 'updated_age'],
      dtype='object')


data.shape

(20801, 16)


#feature - Sqft_living
x = data.iloc[:,[1]].values
y = data.iloc[:,[0]].values
x= np.append(arr=np.ones((20801,1)).astype(int),values = x,axis = 1)
regressor_OLS=sm.OLS(endog=y,exog=x).fit()
regressor_OLS.summary()


##feature - bathrooms
x = data.iloc[:,[2]].values
y = data.iloc[:,[0]].values
x= np.append(arr=np.ones((20801,1)).astype(int),values = x,axis = 1)
regressor_OLS=sm.OLS(endog=y,exog=x).fit()
regressor_OLS.summary()


#feature - bathrooms
x = data.iloc[:,[3]].values
y = data.iloc[:,[0]].values
x= np.append(arr=np.ones((20801,1)).astype(int),values = x,axis = 1)
regressor_OLS=sm.OLS(endog=y,exog=x).fit()
regressor_OLS.summary()


#feature - view
x = data.iloc[:,[4]].values
y = data.iloc[:,[0]].values
x= np.append(arr=np.ones((20801,1)).astype(int),values = x,axis = 1)
regressor_OLS=sm.OLS(endog=y,exog=x).fit()
regressor_OLS.summary()


#feature - bedrooms
x = data.iloc[:,[5]].values
y = data.iloc[:,[0]].values
x= np.append(arr=np.ones((20801,1)).astype(int),values = x,axis = 1)
regressor_OLS=sm.OLS(endog=y,exog=x).fit()
regressor_OLS.summary()


#features - sqft_basement
x = data.iloc[:,[6]].values
y = data.iloc[:,[0]].values
x= np.append(arr=np.ones((20801,1)).astype(int),values = x,axis = 1)
regressor_OLS=sm.OLS(endog=y,exog=x).fit()
regressor_OLS.summary()


#features - waterfront
x = data.iloc[:,[7]].values
y = data.iloc[:,[0]].values
x= np.append(arr=np.ones((20801,1)).astype(int),values = x,axis = 1)
regressor_OLS=sm.OLS(endog=y,exog=x).fit()
regressor_OLS.summary()


#features - floors
x = data.iloc[:,[8]].values
y = data.iloc[:,[0]].values
x= np.append(arr=np.ones((20801,1)).astype(int),values = x,axis = 1)
regressor_OLS=sm.OLS(endog=y,exog=x).fit()
regressor_OLS.summary()


#features - lat
x = data.iloc[:,[9]].values
y = data.iloc[:,[0]].values
x= np.append(arr=np.ones((20801,1)).astype(int),values = x,axis = 1)
regressor_OLS=sm.OLS(endog=y,exog=x).fit()
regressor_OLS.summary()


#features - updated_age
x = data.iloc[:,[10]].values
y = data.iloc[:,[0]].values
x= np.append(arr=np.ones((20801,1)).astype(int),values = x,axis = 1)
regressor_OLS=sm.OLS(endog=y,exog=x).fit()
regressor_OLS.summary()


#features - updated_age
x = data.iloc[:,[11]].values
y = data.iloc[:,[0]].values
x= np.append(arr=np.ones((20801,1)).astype(int),values = x,axis = 1)
regressor_OLS=sm.OLS(endog=y,exog=x).fit()
regressor_OLS.summary()


#features - updated_age
x = data.iloc[:,[12]].values
y = data.iloc[:,[0]].values
x= np.append(arr=np.ones((20801,1)).astype(int),values = x,axis = 1)
regressor_OLS=sm.OLS(endog=y,exog=x).fit()
regressor_OLS.summary()


#features - updated_age
x = data.iloc[:,[13]].values
y = data.iloc[:,[0]].values
x= np.append(arr=np.ones((20801,1)).astype(int),values = x,axis = 1)
regressor_OLS=sm.OLS(endog=y,exog=x).fit()
regressor_OLS.summary()


#features - updated_age
x = data.iloc[:,[14]].values
y = data.iloc[:,[0]].values
x= np.append(arr=np.ones((20801,1)).astype(int),values = x,axis = 1)
regressor_OLS=sm.OLS(endog=y,exog=x).fit()
regressor_OLS.summary()


#features - updated_age
x = data.iloc[:,[15]].values
y = data.iloc[:,[0]].values
x= np.append(arr=np.ones((20801,1)).astype(int),values = x,axis = 1)
regressor_OLS=sm.OLS(endog=y,exog=x).fit()
regressor_OLS.summary()


#Dividing data into X and y variables
y_train = data.pop('price')
X_train = data
from sklearn.feature_selection import RFE
from sklearn.linear_model import LinearRegression
import statsmodels.api as sm
from statsmodels.stats.outliers_influence import variance_inflation_factor
lm = LinearRegression()
lm.fit(X_train,y_train)

LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)


def build_model(X,y):
  X = sm.add_constant(X) #Adding the constant
  lm = sm.OLS(y,X).fit() # fitting the model
  print(lm.summary()) # model summary
  return X


def checkVIF(X):
  vif = pd.DataFrame()
  vif['Features'] = X.columns
  vif['VIF'] = [variance_inflation_factor(X.values, i) for i in range(X.shape[1])]
  vif['VIF'] = round(vif['VIF'], 2)
  vif = vif.sort_values(by = "VIF", ascending = False)
  return(vif)


X_train_new = build_model(X_train,y_train)
checkVIF(X_train_new)
X = pd.DataFrame(X_train)
y = pd.DataFrame(y_train)
model = sm.OLS(y, sm.add_constant(X))
model_fit = model.fit()

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                  price   R-squared:                       0.687
Model:                            OLS   Adj. R-squared:                  0.686
Method:                 Least Squares   F-statistic:                     3035.
Date:                Sat, 25 Sep 2021   Prob (F-statistic):               0.00
Time:                        02:12:56   Log-Likelihood:            -2.8418e+05
No. Observations:               20801   AIC:                         5.684e+05
Df Residuals:                   20785   BIC:                         5.685e+05
Df Model:                          15                                         
Covariance Type:            nonrobust                                         
=================================================================================
                    coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------
const         -4.727e+07   1.59e+06    -29.814      0.000   -5.04e+07   -4.42e+07
bedrooms      -3.746e+04   2092.043    -17.907      0.000   -4.16e+04   -3.34e+04
bathrooms       3.96e+04   3474.184     11.397      0.000    3.28e+04    4.64e+04
sqft_living     193.8176      3.929     49.330      0.000     186.117     201.519
sqft_lot          0.1354      0.049      2.738      0.006       0.038       0.232
floors        -1.331e+04   4072.708     -3.268      0.001   -2.13e+04   -5327.913
waterfront     6.091e+05   1.81e+04     33.728      0.000    5.74e+05    6.44e+05
view           5.439e+04   2221.049     24.486      0.000       5e+04    5.87e+04
condition      3.072e+04   2426.242     12.660      0.000     2.6e+04    3.55e+04
grade          9.015e+04   2264.994     39.801      0.000    8.57e+04    9.46e+04
sqft_basement   -38.6095      4.653     -8.298      0.000     -47.729     -29.490
lat            5.805e+05   1.09e+04     53.503      0.000    5.59e+05    6.02e+05
long          -1.549e+05   1.24e+04    -12.501      0.000   -1.79e+05   -1.31e+05
sqft_living15    23.4865      3.576      6.569      0.000      16.478      30.495
sqft_lot15       -0.3894      0.076     -5.149      0.000      -0.538      -0.241
updated_age    2039.7298     74.964     27.209      0.000    1892.794    2186.666
==============================================================================
Omnibus:                    17667.070   Durbin-Watson:                   1.994
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1699605.539
Skew:                           3.576   Prob(JB):                         0.00
Kurtosis:                      46.702   Cond. No.                     5.68e+07
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 5.68e+07. This might indicate that there are
strong multicollinearity or other numerical problems.


# create dataframe from X, y for easier plot handling
dataframe = pd.concat([X, y], axis=1)


# model values
model_fitted_y = model_fit.fittedvalues


# model residuals
model_residuals = model_fit.resid


# normalized residuals
model_norm_residuals = model_fit.get_influence().resid_studentized_internal


# absolute squared normalized residuals
model_norm_residuals_abs_sqrt = np.sqrt(np.abs(model_norm_residuals))


# absolute residuals
model_abs_resid = np.abs(model_residuals)


# leverage, from statsmodels internals
model_leverage = model_fit.get_influence().hat_matrix_diag


# cook's distance, from statsmodels internals
model_cooks = model_fit.get_influence().cooks_distance[0]
plot_lm_1 = plt.figure()
plot_lm_1.axes[0] = sns.residplot(model_fitted_y, dataframe.columns[-1], data=dataframe,
               lowess=True,
               scatter_kws={'alpha': 0.5},
               line_kws={'color': 'red', 'lw': 1, 'alpha': 0.8})
plot_lm_1.axes[0].set_title('Residuals vs Fitted')
plot_lm_1.axes[0].set_xlabel('Fitted values')
plot_lm_1.axes[0].set_ylabel('Residuals');

X_train_new = build_model(X_train_new,y_train)
checkVIF(X_train_new)

/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  FutureWarning

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                  price   R-squared:                       0.687
Model:                            OLS   Adj. R-squared:                  0.686
Method:                 Least Squares   F-statistic:                     3035.
Date:                Fri, 24 Sep 2021   Prob (F-statistic):               0.00
Time:                        22:56:59   Log-Likelihood:            -2.8418e+05
No. Observations:               20801   AIC:                         5.684e+05
Df Residuals:                   20785   BIC:                         5.685e+05
Df Model:                          15                                         
Covariance Type:            nonrobust                                         
=================================================================================
                    coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------
const         -4.727e+07   1.59e+06    -29.814      0.000   -5.04e+07   -4.42e+07
bedrooms      -3.746e+04   2092.043    -17.907      0.000   -4.16e+04   -3.34e+04
bathrooms       3.96e+04   3474.184     11.397      0.000    3.28e+04    4.64e+04
sqft_living     193.8176      3.929     49.330      0.000     186.117     201.519
sqft_lot          0.1354      0.049      2.738      0.006       0.038       0.232
floors        -1.331e+04   4072.708     -3.268      0.001   -2.13e+04   -5327.913
waterfront     6.091e+05   1.81e+04     33.728      0.000    5.74e+05    6.44e+05
view           5.439e+04   2221.049     24.486      0.000       5e+04    5.87e+04
condition      3.072e+04   2426.242     12.660      0.000     2.6e+04    3.55e+04
grade          9.015e+04   2264.994     39.801      0.000    8.57e+04    9.46e+04
sqft_basement   -38.6095      4.653     -8.298      0.000     -47.729     -29.490
lat            5.805e+05   1.09e+04     53.503      0.000    5.59e+05    6.02e+05
long          -1.549e+05   1.24e+04    -12.501      0.000   -1.79e+05   -1.31e+05
sqft_living15    23.4865      3.576      6.569      0.000      16.478      30.495
sqft_lot15       -0.3894      0.076     -5.149      0.000      -0.538      -0.241
updated_age    2039.7298     74.964     27.209      0.000    1892.794    2186.666
==============================================================================
Omnibus:                    17667.070   Durbin-Watson:                   1.994
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1699605.539
Skew:                           3.576   Prob(JB):                         0.00
Kurtosis:                      46.702   Cond. No.                     5.68e+07
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 5.68e+07. This might indicate that there are
strong multicollinearity or other numerical problems.


X_train_new = X_train_new.drop(["long"], axis = 1)
X_train_new = build_model(X_train_new,y_train)
checkVIF(X_train_new)

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                  price   R-squared:                       0.684
Model:                            OLS   Adj. R-squared:                  0.684
Method:                 Least Squares   F-statistic:                     3217.
Date:                Sat, 25 Sep 2021   Prob (F-statistic):               0.00
Time:                        02:13:40   Log-Likelihood:            -2.8426e+05
No. Observations:               20801   AIC:                         5.686e+05
Df Residuals:                   20786   BIC:                         5.687e+05
Df Model:                          14                                         
Covariance Type:            nonrobust                                         
=================================================================================
                    coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------
const         -2.852e+07   5.15e+05    -55.340      0.000   -2.95e+07   -2.75e+07
bedrooms      -3.763e+04   2099.798    -17.922      0.000   -4.17e+04   -3.35e+04
bathrooms      3.986e+04   3487.073     11.430      0.000     3.3e+04    4.67e+04
sqft_living     190.1095      3.932     48.345      0.000     182.402     197.817
sqft_lot          0.0880      0.050      1.779      0.075      -0.009       0.185
floors        -9045.3031   4073.518     -2.221      0.026    -1.7e+04   -1060.889
waterfront      6.13e+05   1.81e+04     33.826      0.000    5.77e+05    6.49e+05
view           5.721e+04   2217.724     25.799      0.000    5.29e+04    6.16e+04
condition      2.883e+04   2430.564     11.860      0.000    2.41e+04    3.36e+04
grade          9.407e+04   2251.481     41.783      0.000    8.97e+04    9.85e+04
sqft_basement   -28.2706      4.596     -6.151      0.000     -37.279     -19.263
lat            5.839e+05   1.09e+04     53.635      0.000    5.63e+05    6.05e+05
sqft_living15    13.8846      3.505      3.961      0.000       7.014      20.755
sqft_lot15       -0.4732      0.076     -6.258      0.000      -0.621      -0.325
updated_age    2337.9144     71.333     32.775      0.000    2198.096    2477.733
==============================================================================
Omnibus:                    17805.209   Durbin-Watson:                   1.993
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1714768.591
Skew:                           3.624   Prob(JB):                         0.00
Kurtosis:                      46.886   Cond. No.                     1.84e+07
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.84e+07. This might indicate that there are
strong multicollinearity or other numerical problems.


X_train_new = X_train_new.drop(["sqft_lot"], axis = 1)
X_train_new = build_model(X_train_new,y_train)
checkVIF(X_train_new)

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                  price   R-squared:                       0.684
Model:                            OLS   Adj. R-squared:                  0.684
Method:                 Least Squares   F-statistic:                     3464.
Date:                Sat, 25 Sep 2021   Prob (F-statistic):               0.00
Time:                        02:14:23   Log-Likelihood:            -2.8426e+05
No. Observations:               20801   AIC:                         5.686e+05
Df Residuals:                   20787   BIC:                         5.687e+05
Df Model:                          13                                         
Covariance Type:            nonrobust                                         
=================================================================================
                    coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------
const         -2.849e+07   5.15e+05    -55.310      0.000   -2.95e+07   -2.75e+07
bedrooms      -3.773e+04   2099.180    -17.974      0.000   -4.18e+04   -3.36e+04
bathrooms      3.991e+04   3487.110     11.446      0.000    3.31e+04    4.67e+04
sqft_living     190.6164      3.922     48.599      0.000     182.929     198.304
floors        -9299.5522   4071.221     -2.284      0.022   -1.73e+04   -1319.641
waterfront     6.124e+05   1.81e+04     33.797      0.000    5.77e+05    6.48e+05
view           5.732e+04   2216.983     25.857      0.000     5.3e+04    6.17e+04
condition      2.876e+04   2430.390     11.833      0.000     2.4e+04    3.35e+04
grade           9.41e+04   2251.540     41.795      0.000    8.97e+04    9.85e+04
sqft_basement   -28.6705      4.591     -6.246      0.000     -37.668     -19.673
lat            5.832e+05   1.09e+04     53.603      0.000    5.62e+05    6.05e+05
sqft_living15    13.5670      3.501      3.875      0.000       6.705      20.429
sqft_lot15       -0.3792      0.054     -7.012      0.000      -0.485      -0.273
updated_age    2340.9640     71.316     32.825      0.000    2201.179    2480.749
==============================================================================
Omnibus:                    17787.397   Durbin-Watson:                   1.993
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1706676.767
Skew:                           3.619   Prob(JB):                         0.00
Kurtosis:                      46.781   Cond. No.                     1.10e+07
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.1e+07. This might indicate that there are
strong multicollinearity or other numerical problems.


X_train_new = X_train_new.drop(["condition"], axis = 1)
X_train_new = build_model(X_train_new,y_train)
checkVIF(X_train_new)

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                  price   R-squared:                       0.682
Model:                            OLS   Adj. R-squared:                  0.682
Method:                 Least Squares   F-statistic:                     3716.
Date:                Sat, 25 Sep 2021   Prob (F-statistic):               0.00
Time:                        02:15:53   Log-Likelihood:            -2.8433e+05
No. Observations:               20801   AIC:                         5.687e+05
Df Residuals:                   20788   BIC:                         5.688e+05
Df Model:                          12                                         
Covariance Type:            nonrobust                                         
=================================================================================
                    coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------
const         -2.789e+07   5.14e+05    -54.236      0.000   -2.89e+07   -2.69e+07
bedrooms      -3.664e+04   2104.156    -17.413      0.000   -4.08e+04   -3.25e+04
bathrooms      4.317e+04   3487.835     12.377      0.000    3.63e+04       5e+04
sqft_living     189.5590      3.934     48.181      0.000     181.847     197.271
floors        -1.277e+04   4074.184     -3.135      0.002   -2.08e+04   -4786.848
waterfront     6.144e+05   1.82e+04     33.798      0.000    5.79e+05     6.5e+05
view           5.723e+04   2224.369     25.729      0.000    5.29e+04    6.16e+04
grade          9.475e+04   2258.382     41.957      0.000    9.03e+04    9.92e+04
sqft_basement   -25.0629      4.596     -5.454      0.000     -34.071     -16.055
lat            5.724e+05   1.09e+04     52.622      0.000    5.51e+05    5.94e+05
sqft_living15    12.7671      3.512      3.636      0.000       5.884      19.650
sqft_lot15       -0.3697      0.054     -6.816      0.000      -0.476      -0.263
updated_age    2615.7708     67.654     38.664      0.000    2483.164    2748.378
==============================================================================
Omnibus:                    17583.982   Durbin-Watson:                   1.993
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1635514.781
Skew:                           3.560   Prob(JB):                         0.00
Kurtosis:                      45.853   Cond. No.                     1.09e+07
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.09e+07. This might indicate that there are
strong multicollinearity or other numerical problems.


data.columns

Index(['bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors',
       'waterfront', 'view', 'condition', 'grade', 'sqft_basement', 'lat',
       'long', 'sqft_living15', 'sqft_lot15', 'updated_age'],
      dtype='object')


X_train_new = X_train_new.drop(["sqft_lot15"], axis = 1)
X_train_new = build_model(X_train_new,y_train)
checkVIF(X_train_new)

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                  price   R-squared:                       0.681
Model:                            OLS   Adj. R-squared:                  0.681
Method:                 Least Squares   F-statistic:                     4040.
Date:                Sat, 25 Sep 2021   Prob (F-statistic):               0.00
Time:                        02:16:36   Log-Likelihood:            -2.8436e+05
No. Observations:               20801   AIC:                         5.687e+05
Df Residuals:                   20789   BIC:                         5.688e+05
Df Model:                          11                                         
Covariance Type:            nonrobust                                         
=================================================================================
                    coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------
const         -2.817e+07   5.13e+05    -54.878      0.000   -2.92e+07   -2.72e+07
bedrooms      -3.532e+04   2097.472    -16.837      0.000   -3.94e+04   -3.12e+04
bathrooms      4.385e+04   3490.236     12.562      0.000     3.7e+04    5.07e+04
sqft_living     185.2078      3.886     47.655      0.000     177.590     192.826
floors        -1.005e+04   4058.971     -2.476      0.013    -1.8e+04   -2093.117
waterfront     6.148e+05   1.82e+04     33.782      0.000    5.79e+05     6.5e+05
view            5.69e+04   2226.258     25.557      0.000    5.25e+04    6.13e+04
grade          9.553e+04   2257.995     42.306      0.000    9.11e+04       1e+05
sqft_basement   -22.0609      4.579     -4.817      0.000     -31.037     -13.085
lat            5.779e+05   1.09e+04     53.222      0.000    5.57e+05    5.99e+05
sqft_living15    11.6169      3.512      3.308      0.001       4.734      18.500
updated_age    2631.6736     67.688     38.880      0.000    2499.000    2764.347
==============================================================================
Omnibus:                    17681.398   Durbin-Watson:                   1.993
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1675898.494
Skew:                           3.586   Prob(JB):                         0.00
Kurtosis:                      46.384   Cond. No.                     1.10e+06
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.1e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


X_train_new = X_train_new.drop(["updated_age"], axis = 1)
X_train_new = build_model(X_train_new,y_train)
checkVIF(X_train_new)

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                  price   R-squared:                       0.658
Model:                            OLS   Adj. R-squared:                  0.658
Method:                 Least Squares   F-statistic:                     4002.
Date:                Sat, 25 Sep 2021   Prob (F-statistic):               0.00
Time:                        02:18:22   Log-Likelihood:            -2.8509e+05
No. Observations:               20801   AIC:                         5.702e+05
Df Residuals:                   20790   BIC:                         5.703e+05
Df Model:                          10                                         
Covariance Type:            nonrobust                                         
=================================================================================
                    coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------
const         -3.235e+07    5.2e+05    -62.229      0.000   -3.34e+07   -3.13e+07
bedrooms      -2.961e+04   2167.016    -13.665      0.000   -3.39e+04   -2.54e+04
bathrooms     -2683.0388   3395.683     -0.790      0.429   -9338.842    3972.765
sqft_living     198.1978      4.010     49.423      0.000     190.337     206.058
floors        -3.409e+04   4154.788     -8.205      0.000   -4.22e+04   -2.59e+04
waterfront     6.078e+05   1.88e+04     32.249      0.000    5.71e+05    6.45e+05
view           6.762e+04   2287.952     29.555      0.000    6.31e+04    7.21e+04
grade          8.088e+04   2305.804     35.076      0.000    7.64e+04    8.54e+04
sqft_basement    -4.6312      4.720     -0.981      0.327     -13.883       4.621
lat            6.725e+05    1.1e+04     61.351      0.000    6.51e+05    6.94e+05
sqft_living15     4.1177      3.631      1.134      0.257      -3.000      11.236
==============================================================================
Omnibus:                    17310.306   Durbin-Watson:                   1.991
Prob(Omnibus):                  0.000   Jarque-Bera (JB):          1453782.513
Skew:                           3.503   Prob(JB):                         0.00
Kurtosis:                      43.352   Cond. No.                     1.08e+06
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.08e+06. This might indicate that there are
strong multicollinearity or other numerical problems.


model_fitted_y = model_fit.fittedvalues


model_residuals = model_fit.resid


# normalized residuals
model_norm_residuals = model_fit.get_influence().resid_studentized_internal


# absolute squared normalized residuals
model_norm_residuals_abs_sqrt = np.sqrt(np.abs(model_norm_residuals))


# absolute residuals
model_abs_resid = np.abs(model_residuals)


# leverage, from statsmodels internals
model_leverage = model_fit.get_influence().hat_matrix_diag


# cook's distance, from statsmodels internals
model_cooks = model_fit.get_influence().cooks_distance[0]
plot_lm_1 = plt.figure()
plot_lm_1.axes[0] = sns.residplot(model_fitted_y, dataframe.columns[-1], data=dataframe,
 lowess=True,
 scatter_kws={'alpha': 0.5},
 line_kws={'color': 'red', 'lw': 1, 'alpha': 0.8})
plot_lm_1.axes[0].set_title('Residuals vs Fitted')
plot_lm_1.axes[0].set_xlabel('Fitted values')
plot_lm_1.axes[0].set_ylabel('Residuals');

/usr/local/lib/python3.7/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  FutureWarning


list(0.1,0.28,0.494,0.008,0.082,0.072,0.158,0.001,0.449,0.13,0.098,0.000,0.345,0.007,0.014)

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-22-bd72e5580686> in <module>()
----> 1 list(0.1,0.28,0.494,0.008,0.082,0.072,0.158,0.001,0.449,0.13,0.098,0.000,0.345,0.007,0.014)

TypeError: list expected at most 1 arguments, got 15

	id	date	price	bedrooms	bathrooms	sqft_living	sqft_lot	floors	view	condition	grade	sqft_above	sqft_basement	yr_built	yr_renovated	zipcode	lat	long	sqft_living15	sqft_lot15
0	7129300520	20141013T000000	221900.0	3	1.00	1180	5650	1.0	0	3	7	1180	0	1955	0	98178	47.5112	-122.257	1340	5650
1	6414100192	20141209T000000	538000.0	3	2.25	2570	7242	2.0	0	3	7	2170	400	1951	1991	98125	47.7210	-122.319	1690	7639
2	5631500400	20150225T000000	180000.0	2	1.00	770	10000	1.0	0	3	6	770	0	1933	0	98028	47.7379	-122.233	2720	8062
3	2487200875	20141209T000000	604000.0	4	3.00	1960	5000	1.0	0	5	7	1050	910	1965	0	98136	47.5208	-122.393	1360	5000
4	1954400510	20150218T000000	510000.0	3	2.00	1680	8080	1.0	0	3	8	1680	0	1987	0	98074	47.6168	-122.045	1800	7503
5	7237550310	20140512T000000	1225000.0	4	4.50	5420	101930	1.0	0	3	11	3890	1530	2001	0	98053	47.6561	-122.005	4760	101930
6	1321400060	20140627T000000	257500.0	3	2.25	1715	6819	2.0	0	3	7	1715	0	1995	0	98003	47.3097	-122.327	2238	6819
7	2008000270	20150115T000000	291850.0	3	1.50	1060	9711	1.0	0	3	7	1060	0	1963	0	98198	47.4095	-122.315	1650	9711
8	2414600126	20150415T000000	229500.0	3	1.00	1780	7470	1.0	0	3	7	1050	730	1960	0	98146	47.5123	-122.337	1780	8113
9	3793500160	20150312T000000	323000.0	3	2.50	1890	6560	2.0	0	3	7	1890	0	2003	0	98038	47.3684	-122.031	2390	7570
10	1736800520	20150403T000000	662500.0	3	2.50	3560	9796	1.0	0	3	8	1860	1700	1965	0	98007	47.6007	-122.145	2210	8925
11	9212900260	20140527T000000	468000.0	2	1.00	1160	6000	1.0	0	4	7	860	300	1942	0	98115	47.6900	-122.292	1330	6000
12	114101516	20140528T000000	310000.0	3	1.00	1430	19901	1.5	0	4	7	1430	0	1927	0	98028	47.7558	-122.229	1780	12697
13	6054650070	20141007T000000	400000.0	3	1.75	1370	9680	1.0	0	4	7	1370	0	1977	0	98074	47.6127	-122.045	1370	10208
14	1175000570	20150312T000000	530000.0	5	2.00	1810	4850	1.5	0	3	7	1810	0	1900	0	98107	47.6700	-122.394	1360	4850
15	9297300055	20150124T000000	650000.0	4	3.00	2950	5000	2.0	3	3	9	1980	970	1979	0	98126	47.5714	-122.375	2140	4000
16	1875500060	20140731T000000	395000.0	3	2.00	1890	14040	2.0	0	3	7	1890	0	1994	0	98019	47.7277	-121.962	1890	14018
17	6865200140	20140529T000000	485000.0	4	1.00	1600	4300	1.5	0	4	7	1600	0	1916	0	98103	47.6648	-122.343	1610	4300
18	16000397	20141205T000000	189000.0	2	1.00	1200	9850	1.0	0	4	7	1200	0	1921	0	98002	47.3089	-122.210	1060	5095
19	7983200060	20150424T000000	230000.0	3	1.00	1250	9774	1.0	0	4	7	1250	0	1969	0	98003	47.3343	-122.306	1280	8850

	id	price	bedrooms	bathrooms	sqft_living	sqft_lot	floors	waterfront	view	condition	grade	sqft_above	sqft_basement	yr_built	yr_renovated	zipcode	lat	long	sqft_living15	sqft_lot15
count	2.161300e+04	2.161300e+04	21613.000000	21613.000000	21613.000000	2.161300e+04	21613.000000	21613.000000	21613.000000	21613.000000	21613.000000	21613.000000	21613.000000	21613.000000	21613.000000	21613.000000	21613.000000	21613.000000	21613.000000	21613.000000
mean	4.580302e+09	5.400881e+05	3.370842	2.114757	2079.899736	1.510697e+04	1.494309	0.007542	0.234303	3.409430	7.656873	1788.390691	291.509045	1971.005136	84.402258	98077.939805	47.560053	-122.213896	1986.552492	12768.455652
std	2.876566e+09	3.671272e+05	0.930062	0.770163	918.440897	4.142051e+04	0.539989	0.086517	0.766318	0.650743	1.175459	828.090978	442.575043	29.373411	401.679240	53.505026	0.138564	0.140828	685.391304	27304.179631
min	1.000102e+06	7.500000e+04	0.000000	0.000000	290.000000	5.200000e+02	1.000000	0.000000	0.000000	1.000000	1.000000	290.000000	0.000000	1900.000000	0.000000	98001.000000	47.155900	-122.519000	399.000000	651.000000
25%	2.123049e+09	3.219500e+05	3.000000	1.750000	1427.000000	5.040000e+03	1.000000	0.000000	0.000000	3.000000	7.000000	1190.000000	0.000000	1951.000000	0.000000	98033.000000	47.471000	-122.328000	1490.000000	5100.000000
50%	3.904930e+09	4.500000e+05	3.000000	2.250000	1910.000000	7.618000e+03	1.500000	0.000000	0.000000	3.000000	7.000000	1560.000000	0.000000	1975.000000	0.000000	98065.000000	47.571800	-122.230000	1840.000000	7620.000000
75%	7.308900e+09	6.450000e+05	4.000000	2.500000	2550.000000	1.068800e+04	2.000000	0.000000	0.000000	4.000000	8.000000	2210.000000	560.000000	1997.000000	0.000000	98118.000000	47.678000	-122.125000	2360.000000	10083.000000
max	9.900000e+09	7.700000e+06	33.000000	8.000000	13540.000000	1.651359e+06	3.500000	1.000000	4.000000	5.000000	13.000000	9410.000000	4820.000000	2015.000000	2015.000000	98199.000000	47.777600	-121.315000	6210.000000	871200.000000

	id	date	price	bedrooms	bathrooms	sqft_living	sqft_lot	floors	condition	grade	sqft_above	sqft_basement	yr_built	yr_renovated	zipcode	lat	long	sqft_living15	sqft_lot15	years
0	7129300520	20141013T000000	221900.0	3	1.00	1180	5650	1.0	3	7	1180	0	1955	0	98178	47.5112	-122.257	1340	5650	2014
1	6414100192	20141209T000000	538000.0	3	2.25	2570	7242	2.0	3	7	2170	400	1951	1991	98125	47.7210	-122.319	1690	7639	2014
2	5631500400	20150225T000000	180000.0	2	1.00	770	10000	1.0	3	6	770	0	1933	0	98028	47.7379	-122.233	2720	8062	2015
3	2487200875	20141209T000000	604000.0	4	3.00	1960	5000	1.0	5	7	1050	910	1965	0	98136	47.5208	-122.393	1360	5000	2014
4	1954400510	20150218T000000	510000.0	3	2.00	1680	8080	1.0	3	8	1680	0	1987	0	98074	47.6168	-122.045	1800	7503	2015

	id	date	price	bedrooms	bathrooms	sqft_living	sqft_lot	floors	condition	grade	sqft_above	sqft_basement	yr_built	yr_renovated	zipcode	lat	long	sqft_living15	sqft_lot15	years	age
0	7129300520	20141013T000000	221900.0	3	1.00	1180	5650	1.0	3	7	1180	0	1955	0	98178	47.5112	-122.257	1340	5650	2014	59
1	6414100192	20141209T000000	538000.0	3	2.25	2570	7242	2.0	3	7	2170	400	1951	1991	98125	47.7210	-122.319	1690	7639	2014	63
2	5631500400	20150225T000000	180000.0	2	1.00	770	10000	1.0	3	6	770	0	1933	0	98028	47.7379	-122.233	2720	8062	2015	82
3	2487200875	20141209T000000	604000.0	4	3.00	1960	5000	1.0	5	7	1050	910	1965	0	98136	47.5208	-122.393	1360	5000	2014	49
4	1954400510	20150218T000000	510000.0	3	2.00	1680	8080	1.0	3	8	1680	0	1987	0	98074	47.6168	-122.045	1800	7503	2015	28

	id	date	price	bedrooms	bathrooms	sqft_living	sqft_lot	floors	condition	grade	sqft_above	sqft_basement	yr_built	yr_renovated	zipcode	lat	long	sqft_living15	sqft_lot15	years	age	updated_age
0	7129300520	20141013T000000	221900.0	3	1.00	1180	5650	1.0	3	7	1180	0	1955	0	98178	47.5112	-122.257	1340	5650	2014	59	59
1	6414100192	20141209T000000	538000.0	3	2.25	2570	7242	2.0	3	7	2170	400	1951	1991	98125	47.7210	-122.319	1690	7639	2014	63	23
2	5631500400	20150225T000000	180000.0	2	1.00	770	10000	1.0	3	6	770	0	1933	0	98028	47.7379	-122.233	2720	8062	2015	82	82
3	2487200875	20141209T000000	604000.0	4	3.00	1960	5000	1.0	5	7	1050	910	1965	0	98136	47.5208	-122.393	1360	5000	2014	49	49
4	1954400510	20150218T000000	510000.0	3	2.00	1680	8080	1.0	3	8	1680	0	1987	0	98074	47.6168	-122.045	1800	7503	2015	28	28

	price	bedrooms	bathrooms	sqft_living	sqft_lot	floors	view	condition	grade	sqft_above	sqft_basement	lat	long	sqft_living15	sqft_lot15	age	updated_age
4035	2150000.0	8	6.00	4340	9415	2.0	0	3	8	4340	0	47.6316	-122.202	2050	9100	47	47
4067	373000.0	8	3.00	2850	12714	1.0	0	3	7	2850	0	47.4859	-122.205	1480	4942	56	56
6174	340000.0	8	2.75	2790	6695	1.0	0	3	7	1470	1320	47.7565	-122.331	1760	7624	37	37
9077	700000.0	8	2.50	2280	3000	1.5	0	3	7	1210	1070	47.6675	-122.316	1610	3000	104	104
9452	900000.0	8	4.00	4020	7500	1.0	0	3	8	2010	2010	47.6732	-122.363	1560	3737	46	46
10958	1650000.0	8	2.75	4040	20666	1.0	0	4	9	2020	2020	47.6340	-122.221	3670	20500	52	52
12885	808000.0	8	3.75	3460	4600	2.0	0	3	7	2860	600	47.6617	-122.289	2170	3750	27	27
15070	430000.0	8	3.25	4300	10441	2.0	0	4	8	2800	1500	47.4786	-122.131	1780	10457	35	35
15670	680000.0	8	2.75	2530	4800	2.0	0	4	7	1390	1140	47.6241	-122.305	1540	4800	113	113
17235	1970000.0	8	3.50	4440	6480	2.0	3	5	10	3140	1300	47.6310	-122.303	4440	8640	55	55
18477	3300000.0	8	4.00	7710	11750	3.5	0	5	12	6090	1620	47.6263	-122.314	4210	8325	110	110
19302	575000.0	8	3.00	3840	15990	1.0	0	3	7	2530	1310	47.7111	-122.211	1380	8172	53	53

Dep. Variable:	y	R-squared:	0.100
Model:	OLS	Adj. R-squared:	0.100
Method:	Least Squares	F-statistic:	2300.
Date:	Sat, 25 Sep 2021	Prob (F-statistic):	0.00
Time:	05:27:33	Log-Likelihood:	-2.9516e+05
No. Observations:	20801	AIC:	5.903e+05
Df Residuals:	20799	BIC:	5.903e+05
Df Model:	1
Covariance Type:	nonrobust

	coef	std err	t	P>\|t\|	[0.025	0.975]
const	9.777e+04	9556.675	10.230	0.000	7.9e+04	1.16e+05
x1	1.309e+05	2730.067	47.962	0.000	1.26e+05	1.36e+05

Omnibus:	18202.324	Durbin-Watson:	1.962
Prob(Omnibus):	0.000	Jarque-Bera (JB):	1110145.551
Skew:	3.939	Prob(JB):	0.00
Kurtosis:	37.912	Cond. No.	14.8

Dep. Variable:	y	R-squared:	0.283
Model:	OLS	Adj. R-squared:	0.283
Method:	Least Squares	F-statistic:	8221.
Date:	Sat, 25 Sep 2021	Prob (F-statistic):	0.00
Time:	05:27:36	Log-Likelihood:	-2.9279e+05
No. Observations:	20801	AIC:	5.856e+05
Df Residuals:	20799	BIC:	5.856e+05
Df Model:	1
Covariance Type:	nonrobust

Omnibus:	16563.116	Durbin-Watson:	1.965
Prob(Omnibus):	0.000	Jarque-Bera (JB):	838166.591
Skew:	3.438	Prob(JB):	0.00
Kurtosis:	33.328	Cond. No.	7.66

Dep. Variable:	y	R-squared:	0.494
Model:	OLS	Adj. R-squared:	0.494
Method:	Least Squares	F-statistic:	2.030e+04
Date:	Sat, 25 Sep 2021	Prob (F-statistic):	0.00
Time:	05:27:39	Log-Likelihood:	-2.8917e+05
No. Observations:	20801	AIC:	5.783e+05
Df Residuals:	20799	BIC:	5.784e+05
Df Model:	1
Covariance Type:	nonrobust

Omnibus:	14336.657	Durbin-Watson:	1.973
Prob(Omnibus):	0.000	Jarque-Bera (JB):	522191.893
Skew:	2.846	Prob(JB):	0.00
Kurtosis:	26.877	Cond. No.	5.68e+03

Dep. Variable:	y	R-squared:	0.008
Model:	OLS	Adj. R-squared:	0.008
Method:	Least Squares	F-statistic:	167.9
Date:	Sat, 25 Sep 2021	Prob (F-statistic):	3.02e-38
Time:	05:27:42	Log-Likelihood:	-2.9617e+05
No. Observations:	20801	AIC:	5.923e+05
Df Residuals:	20799	BIC:	5.924e+05
Df Model:	1
Covariance Type:	nonrobust

Omnibus:	18377.587	Durbin-Watson:	1.965
Prob(Omnibus):	0.000	Jarque-Bera (JB):	1089643.872
Skew:	4.014	Prob(JB):	0.00
Kurtosis:	37.536	Cond. No.	4.79e+04

	coef	std err	t	P>\|t\|	[0.025	0.975]
const	3826.3574	6310.856	0.606	0.544	-8543.413	1.62e+04
x1	2.557e+05	2819.997	90.670	0.000	2.5e+05	2.61e+05

	coef	std err	t	P>\|t\|	[0.025	0.975]
const	5.286e+05	2730.810	193.579	0.000	5.23e+05	5.34e+05
x1	0.7874	0.061	12.957	0.000	0.668	0.906

	coef	std err	t	P>\|t\|	[0.025	0.975]
const	2.342e+05	7514.033	31.172	0.000	2.19e+05	2.49e+05
x1	2.105e+05	4871.800	43.205	0.000	2.01e+05	2.2e+05

	coef	std err	t	P>\|t\|	[0.025	0.975]
const	4.955e+05	2468.028	200.776	0.000	4.91e+05	5e+05
x1	1.911e+05	3057.556	62.486	0.000	1.85e+05	1.97e+05

Dep. Variable:	y	R-squared:	0.082
Model:	OLS	Adj. R-squared:	0.082
Method:	Least Squares	F-statistic:	1867.
Date:	Sat, 25 Sep 2021	Prob (F-statistic):	0.00
Time:	05:27:44	Log-Likelihood:	-2.9536e+05
No. Observations:	20801	AIC:	5.907e+05
Df Residuals:	20799	BIC:	5.907e+05
Df Model:	1
Covariance Type:	nonrobust

Omnibus:	18626.504	Durbin-Watson:	1.981
Prob(Omnibus):	0.000	Jarque-Bera (JB):	1222838.777
Skew:	4.065	Prob(JB):	0.00
Kurtosis:	39.672	Cond. No.	6.53

Dep. Variable:	y	R-squared:	0.072
Model:	OLS	Adj. R-squared:	0.072
Method:	Least Squares	F-statistic:	1611.
Date:	Sat, 25 Sep 2021	Prob (F-statistic):	0.00
Time:	05:27:46	Log-Likelihood:	-2.9547e+05
No. Observations:	20801	AIC:	5.910e+05
Df Residuals:	20799	BIC:	5.910e+05
Df Model:	1
Covariance Type:	nonrobust

Omnibus:	17006.289	Durbin-Watson:	1.959
Prob(Omnibus):	0.000	Jarque-Bera (JB):	873529.323
Skew:	3.584	Prob(JB):	0.00
Kurtosis:	33.927	Cond. No.	11.4

Dep. Variable:	y	R-squared:	0.158
Model:	OLS	Adj. R-squared:	0.158
Method:	Least Squares	F-statistic:	3905.
Date:	Sat, 25 Sep 2021	Prob (F-statistic):	0.00
Time:	05:27:49	Log-Likelihood:	-2.9446e+05
No. Observations:	20801	AIC:	5.889e+05
Df Residuals:	20799	BIC:	5.889e+05
Df Model:	1
Covariance Type:	nonrobust

Omnibus:	17167.806	Durbin-Watson:	1.959
Prob(Omnibus):	0.000	Jarque-Bera (JB):	973094.774
Skew:	3.601	Prob(JB):	0.00
Kurtosis:	35.724	Cond. No.	1.45

Dep. Variable:	y	R-squared:	0.001
Model:	OLS	Adj. R-squared:	0.001
Method:	Least Squares	F-statistic:	20.63
Date:	Sat, 25 Sep 2021	Prob (F-statistic):	5.60e-06
Time:	05:27:54	Log-Likelihood:	-2.9624e+05
No. Observations:	20801	AIC:	5.925e+05
Df Residuals:	20799	BIC:	5.925e+05
Df Model:	1
Covariance Type:	nonrobust

Omnibus:	18353.561	Durbin-Watson:	1.964
Prob(Omnibus):	0.000	Jarque-Bera (JB):	1078313.052
Skew:	4.009	Prob(JB):	0.00
Kurtosis:	37.349	Cond. No.	20.0

Dep. Variable:	y	R-squared:	0.449
Model:	OLS	Adj. R-squared:	0.449
Method:	Least Squares	F-statistic:	1.692e+04
Date:	Sat, 25 Sep 2021	Prob (F-statistic):	0.00
Time:	05:28:00	Log-Likelihood:	-2.9006e+05
No. Observations:	20801	AIC:	5.801e+05
Df Residuals:	20799	BIC:	5.801e+05
Df Model:	1
Covariance Type:	nonrobust

Omnibus:	19162.609	Durbin-Watson:	1.975
Prob(Omnibus):	0.000	Jarque-Bera (JB):	1973458.532
Skew:	4.086	Prob(JB):	0.00
Kurtosis:	50.013	Cond. No.	51.2

Normalization of the features¶

Dep. Variable:	y	R-squared:	0.103
Model:	OLS	Adj. R-squared:	0.103
Method:	Least Squares	F-statistic:	2384.
Date:	Sat, 25 Sep 2021	Prob (F-statistic):	0.00
Time:	05:28:04	Log-Likelihood:	-2.9512e+05
No. Observations:	20801	AIC:	5.902e+05
Df Residuals:	20799	BIC:	5.903e+05
Df Model:	1
Covariance Type:	nonrobust

Omnibus:	17245.218	Durbin-Watson:	1.950
Prob(Omnibus):	0.000	Jarque-Bera (JB):	843777.433
Skew:	3.686	Prob(JB):	0.00
Kurtosis:	33.318	Cond. No.	640.

Dep. Variable:	y	R-squared:	0.098
Model:	OLS	Adj. R-squared:	0.098
Method:	Least Squares	F-statistic:	2255.
Date:	Sat, 25 Sep 2021	Prob (F-statistic):	0.00
Time:	05:28:16	Log-Likelihood:	-2.9518e+05
No. Observations:	20801	AIC:	5.904e+05
Df Residuals:	20799	BIC:	5.904e+05
Df Model:	1
Covariance Type:	nonrobust

Omnibus:	19535.299	Durbin-Watson:	1.968
Prob(Omnibus):	0.000	Jarque-Bera (JB):	1449685.117
Skew:	4.357	Prob(JB):	0.00
Kurtosis:	42.959	Cond. No.	1.62e+04

Omnibus:	18369.822	Durbin-Watson:	1.966
Prob(Omnibus):	0.000	Jarque-Bera (JB):	1079256.989
Skew:	4.015	Prob(JB):	0.00
Kurtosis:	37.362	Cond. No.	1.06e+05

Dep. Variable:	y	R-squared:	0.345
Model:	OLS	Adj. R-squared:	0.345
Method:	Least Squares	F-statistic:	1.095e+04
Date:	Sat, 25 Sep 2021	Prob (F-statistic):	0.00
Time:	02:12:38	Log-Likelihood:	-2.9185e+05
No. Observations:	20801	AIC:	5.837e+05
Df Residuals:	20799	BIC:	5.837e+05
Df Model:	1
Covariance Type:	nonrobust

Omnibus:	19492.457	Durbin-Watson:	1.977
Prob(Omnibus):	0.000	Jarque-Bera (JB):	1856666.629
Skew:	4.240	Prob(JB):	0.00
Kurtosis:	48.501	Cond. No.	6.52e+03

Dep. Variable:	y	R-squared:	0.007
Model:	OLS	Adj. R-squared:	0.007
Method:	Least Squares	F-statistic:	140.5
Date:	Sat, 25 Sep 2021	Prob (F-statistic):	2.64e-32
Time:	02:12:41	Log-Likelihood:	-2.9618e+05
No. Observations:	20801	AIC:	5.924e+05
Df Residuals:	20799	BIC:	5.924e+05
Df Model:	1
Covariance Type:	nonrobust

Omnibus:	18364.549	Durbin-Watson:	1.965
Prob(Omnibus):	0.000	Jarque-Bera (JB):	1084425.463
Skew:	4.011	Prob(JB):	0.00
Kurtosis:	37.451	Cond. No.	3.40e+04

Dep. Variable:	y	R-squared:	0.014
Model:	OLS	Adj. R-squared:	0.014
Method:	Least Squares	F-statistic:	295.3
Date:	Sat, 25 Sep 2021	Prob (F-statistic):	1.00e-65
Time:	02:12:43	Log-Likelihood:	-2.9610e+05
No. Observations:	20801	AIC:	5.922e+05
Df Residuals:	20799	BIC:	5.922e+05
Df Model:	1
Covariance Type:	nonrobust